Merton's Jump Diffusion Parameters - Quant Trader Interview Question
Difficulty: Hard
Category: Stochastic Calculus
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Topics: stochastic-calculus, merton-jump-diffusion, jump-process, probability
Problem Description
Merton's jump-diffusion model extends the geometric Brownian motion (GBM) model by incorporating jumps to account for sudden, unexpected price changes. The stochastic differential equation for Merton's jump-diffusion process is given by:
$dS/S = \mu dt + \sigma dW + J dN$
where:
$dS$ is the change in the asset price
$S$ is the asset price
$\mu$ is the drift rate
$dt$ is the change in time
$\sigma$ is the volatility
$dW$ is a Wiener process (Brownian motion)
$dN$ is a Pois
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